Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces
We prove that for every infinite-dimensional Banach space X with a Frechet differentiable norm, the sphere S-X is diffeomorphic to each closed hyperplane in X. We also prove that every infinite-dimensional Banach space Y having a (not necessarily equivalent) C-p norm (with p is an element of N boole...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 1997 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/57010 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/57010 |
| Access Level: | acceso abierto |
| Palabra clave: | 517.986 Infinite-dimensional Banach space Unit sphere Hyperplane Diffeomorphism Funciones (Matemáticas) 1202 Análisis y Análisis Funcional |
| Sumario: | We prove that for every infinite-dimensional Banach space X with a Frechet differentiable norm, the sphere S-X is diffeomorphic to each closed hyperplane in X. We also prove that every infinite-dimensional Banach space Y having a (not necessarily equivalent) C-p norm (with p is an element of N boolean OR {infinity}) is C-p diffeomorphic to Y \ {0}. |
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